Discussion Forum

The normals at three points P, Q and R of the parabola $y^{2}=4ax$ meet at (h,k). The centroid of the $\triangle PQR$ lies on 

Answer:

Explanation:

 The sum of ordinates of feet of normals drawn from a point  to the parabola . $y^{2}=4ax$ is always zero

Now, as normals  at three points p,Q and R of parabola $y^{2}=4ax$  meet at (h,k)

$\Rightarrow$  The normals from (h,k) to $y^{2}=4ax$ meet the parabola at P,Q and R

$\Rightarrow$  y-coordinate $y_{1},y_{2},y_{3}$ of these points and R will be zero

$\Rightarrow$    y-coordinate of the centroid of $\triangle PQR$

i.e, $\frac{y_{1}+y_{2}+y_{3}}{3}=\frac{0}{3}=0$

$\therefore$   centroid lies on y=0